This paper reports on an original work on the study of the behavior of ZnO‐based varistor by ac impedance measurements. The measurements of complex impedance response to small ac signals applied to samples have been achieved in the frequency range 10−3–7×106Hz and a temperature range −196–145 °C. In the temperature range below −120±10 °C, a complete semicircular relaxation phenomenon has been observed, which is in good agreement with the Debye model. In the temperature range above −120±10 °C, the appearance of the depression angle &thgr; may arise from the heterogeneity of the barriers of the ceramic varistor. A Cole–Cole distribution function of the relaxation time constants was used to characterize the response of the ceramic device as a function of temperature. No observable influence in the response was introduced by either the space charge or the electrode. Using the leakage resistance measurements from the complex plane, two values of the activation energies were observed; 0.36±0.02 eV and 0.01±0.001 eV. Similarly, the boundary layer equivalent capacitance measurements detect two other energy levels: 0.06±0.005 eV and about 0 eV.